Not only has the Heat caught the Celtics, it has officially gone past them and into the Eastern Conference final.

Vanquishing the team it couldn't beat for so long with a 16-0 run to end the game, Dwyane Wade scored 34, LeBron James put the Heat up for good with a 3-pointer with 2:10 left on the way to a 33-point effort, and Miami topped Boston 97-87 to win its East semifinal series Wednesday night in five games.

"When you're playing this game, and you have another guy over there doing the things and as capable as LeBron, not only am I a fan on the court, but it makes the game easier," Wade said. "Obviously."

James hit a series-sealing 3-pointer with 40.4 seconds left, then turned and posed for fans.

"They make you fight for everything," James said of the Celtics. "… You can never take a second off against that team."

So he kept playing. A steal and slam six seconds later, followed by a Celtics turnover, got the party started.

Boston was worn down by a younger, more athletic opponent. The Celtics won the first three meetings this season, then lost five of the final six.

Wade was knocked over into courtside seats trying to nab the final rebound, but that only prolonged the moment. James knelt in prayer for several seconds, then ran over to embrace Wade.

"Everything went through my mind at that point," said James, referring to his moment on one knee. "Finally getting over this hump against this team. Everything I went through this summer, with 'The Decision' and deciding to come down here to be a part of this team … because I knew how important team is to this sport … and all the backlash I got from it. I'd be up here for two hours if I tell you exactly everything that went through my head. Very emotional at that point, you know."

Next up for Miami: Chicago or Atlanta, in a series that might start as early as Sunday. Chicago leads 3-2.

Ray Allen led Boston with 18 points, and Rajon Rondo finished with six points in 31 minutes, playing with a brace over the left elbow that he dislocated during Game 3.

"I know we gave a lot in Game 3," Celtics coach Doc Rivers said. "And I don't know if we could ever get that effort back."

Rivers revealed that he "probably will" return for an eighth season. "I don't believe this team is done," he said.

OKLAHOMA CITY — Kevin Durant scored 19, reserve Daequan Cook added 18 and the Thunder followed its triple-overtime triumph with a 99-72 blowout of the Grizzlies to take its first series lead in the Western Conference semifinals.

The Thunder leads 3-2, with Game 6 Friday at Memphis.

Memphis, which matched its lowest point total from the regular season, shot a season-worst 36 percent.